As is well known, it is very difficult to prove the existence of Bose-Einstein condensation for interacting bosons.
Actually, the mathematically rigorous results are still rare. (See, e.g., [1]}, [2]} and references therein.)
In this paper, we present a class of interacting boson models on the \(d\) -dimensional hypercubic lattice for \(d\ge 1\) .
We prove that the models show complete Bose-Einstein condensation for the ground state.
Although the interactions in the Hamiltonians are not necessarily standard, each of them is finite range or
rapidly decays with the diameter of the support.
